On the Wave Resistance of a Two-Dimensional Body at Fixed Froude Numbers

Abstract

The problem of determining the wave resistance created by progressive waves generated by a moving two-dimensional body at fixed Froude numbers is considered. The second dimensionless parameter determining the waves is the dimensionless amplitude defined as the ratio of their amplitude to the wavelength. A variational principle is developed to formulate the problem of nonlinear periodic progressive waves as purely geometric. Using this principle, we have derived an infinite chain of quadratic equations with respect to the Stokes coefficients. The expansion of the wave resistance into power series of amplitude with coefficients depending only on the Froude numbers is performed in analytical form. The results of analytical and exact numerical calculations are compared.